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<article class="li"><h3 class="heading">
<span class="type">Item</span><span class="period">.</span>
</h3>
<p>Within the interval of convergence, <span class="process-math">\(f'(x)\)</span> and <span class="process-math">\(\int f(x)\textrm{d}x\)</span> can be found by term-wise differentiation and integration. For example,</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
f'(x)=\sum_{n=0}^{\infty} na_n(x-x_0)^{n-1}=\sum_{\textcolor{blue}{n=1}}^{\infty} na_n(x-x_0)^{n-1},
\end{equation*}
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<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
f''(x)=\sum_{n=0}^{\infty} n(n-1)a_n(x-x_0)^{n-2}=\sum_{\textcolor{blue}{n=2}}^{\infty} n(n-1)a_n(x-x_0)^{n-2}
\end{equation*}
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